I want to remove the http:// that is added automaticly on the user profile adress

That’s baked into core, and would be difficult to filter out. You’re better off adding a new field specific for what your goal is. It’ll get stored as a text field, and can be used however you please. An example:

function ath_cleanup_profile_fields( $contactmethods ) {

$contactmethods['my_new_profile']   = 'Business Name'; 

    return $contactmethods;
}
add_filter('user_contactmethods','ath_cleanup_profile_fields',10,1);

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